Problem: The following line passes through point $(4, -7)$ : $y = -\dfrac{5}{3} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(4, -7)$ into the equation gives: $-7 = -\dfrac{5}{3} \cdot 4 + b$ $-7 = -\dfrac{20}{3} + b$ $b = -7 + \dfrac{20}{3}$ $b = -\dfrac{1}{3}$ Plugging in $-\dfrac{1}{3}$ for $b$, we get $y = -\dfrac{5}{3} x - \dfrac{1}{3}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(4, -7)$